Question

Proof verification of $x_n = \sqrt[3]{n^3 + 1} - \sqrt{n^2 - 1}$ is bounded

score 106 · Answer 1 · 2026-03-29 03:35:52

106

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Proof verification of $x_n = \sqrt[3]{n^3 + 1} - \sqrt{n^2 - 1}$ is bounded

Published on 29 Mar 2026 - 3:35

score 50 · Answer 2 · 2026-04-09 23:26:35

50

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a few questions on the group structure of G

Published on 09 Apr 2026 - 23:26

score 1.7k · Answer 3 · 2026-03-26 07:35:21

1.7k

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IMO 2017: Determine all functions $f: \mathbb{R} \to\mathbb{R}$ such that, for all real numbers $x$ and $y$, $f(f(x)f(y)) + f(x +y) = f(xy)$.

Published on 26 Mar 2026 - 7:35

score 43 · Answer 4 · 2018-10-23 23:09:03

43

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Is this the correct way to prove that this intersection is a subgroup of Z(G)

Published on 23 Oct 2018 - 23:09

score 222 · Answer 5 · 2026-04-11 15:36:53

222

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Finding a Dominating Function for a Sequence of Function

Published on 11 Apr 2026 - 15:36

score 763 · Answer 6 · 2026-03-30 12:16:27

763

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The category of relations $Rel$ and proving it is isomorphic to its opposite

Published on 30 Mar 2026 - 12:16

score 136 · Answer 7 · 2026-04-01 18:11:45

136

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Show that if $f_{n}$ $\in$ $L^2(a,b)$ and $f_{n} \to f$ in norm, then $(f_{n}, g) \to (f,g)$ for all $g \in L^2(a,b)$.

Published on 01 Apr 2026 - 18:11

score 127 · Answer 8 · 2026-03-27 17:06:10

127

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Set of real values of $k$ such that $4\cdot 2^{2x}-4k\cdot 2^x+5-4k\geq 0$ has a real solution

Published on 27 Mar 2026 - 17:06

score 257 · Answer 9 · 2026-04-09 18:53:07

257

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Proof Compositum of Two Galois extensions is Galois. (Proof Verification)

Published on 09 Apr 2026 - 18:53

score 91 · Answer 10 · 2026-03-28 08:50:04

91

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Simple small o exercises: $1+o(1)=\exp[o(1)]$ and $o[f(x)g(x)]=o[f(x)]O[g(x)]$

Published on 28 Mar 2026 - 8:50

score 209 · Answer 11 · 2018-10-24 13:05:36

209

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Evaluate $\lim\limits_{n \to \infty}\frac{n}{\sqrt[n]{n!}}$.

Published on 24 Oct 2018 - 13:05

score 343 · Answer 12 · 2026-03-26 14:22:18

343

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Is $X=\left\{(x_n)_{n\in\mathbb{N}}\mid x_n\in\{0,1\},\forall n \wedge x_n=1\text{ for at most finitely many $n$}\right\}$ countable or uncountable?

Published on 26 Mar 2026 - 14:22

score 205 · Answer 13 · 2018-10-24 15:25:10

205

Views

Proving $T_0$ is a topological property

Published on 24 Oct 2018 - 15:25

score 30 · Answer 14 · 2026-04-13 17:24:16

30

Views

Calculating simple probabilities of events with multiple unions and intersections:

Published on 13 Apr 2026 - 17:24

score 80 · Answer 15 · 2026-03-28 22:36:51

80

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Proof verification hat $x_n = \{ \sqrt{n^4 + n^3 +1} - \sqrt{n^4 - n^3 + 1} \}$ is an unbounded sequence

Published on 28 Mar 2026 - 22:36

List Question

Proof verification of $x_n = \sqrt[3]{n^3 + 1} - \sqrt{n^2 - 1}$ is bounded

a few questions on the group structure of G

IMO 2017: Determine all functions $f: \mathbb{R} \to\mathbb{R}$ such that, for all real numbers $x$ and $y$, $f(f(x)f(y)) + f(x +y) = f(xy)$.

Is this the correct way to prove that this intersection is a subgroup of Z(G)

Finding a Dominating Function for a Sequence of Function

The category of relations $Rel$ and proving it is isomorphic to its opposite

Show that if $f_{n}$ $\in$ $L^2(a,b)$ and $f_{n} \to f$ in norm, then $(f_{n}, g) \to (f,g)$ for all $g \in L^2(a,b)$.

Set of real values of $k$ such that $4\cdot 2^{2x}-4k\cdot 2^x+5-4k\geq 0$ has a real solution

Proof Compositum of Two Galois extensions is Galois. (Proof Verification)

Simple small o exercises: $1+o(1)=\exp[o(1)]$ and $o[f(x)g(x)]=o[f(x)]O[g(x)]$

Evaluate $\lim\limits_{n \to \infty}\frac{n}{\sqrt[n]{n!}}$.

Is $X=\left\{(x_n)_{n\in\mathbb{N}}\mid x_n\in\{0,1\},\forall n \wedge x_n=1\text{ for at most finitely many $n$}\right\}$ countable or uncountable?

Proving $T_0$ is a topological property

Calculating simple probabilities of events with multiple unions and intersections:

Proof verification hat $x_n = \{ \sqrt{n^4 + n^3 +1} - \sqrt{n^4 - n^3 + 1} \}$ is an unbounded sequence

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